There was no public API, but you can show your automated tests results in the structure using Structure API.
Here is how:
Add issues representing your automated tests to your structure and manually create a test run.
Find the Test Run ID. To do that, open the View drop-down menu -> Manage Views -> mouse over the view name -> Details -> Advanced -> Active Specification
Find Issue IDs. To do that, add “#debug” to the structure board URL, refresh the page and add the Issue ID column.
To send test results to Testy, send HTTP request of the following format:
POST <baseUrl>/rest/testy/1/run/<testRunID>/issue/<issueID>/status Content-type: application/json
Content: { status: "PASSED" }
Replace <baseUrl> with your JIRA url, <testRunID> and <issueID> with the numerical IDs of the test run and the issue respectively. Specify the test result (PASSED, FAILED, BLOCKED,SKIPPED or NONE) in the content part!
To add notes, use the following HTTP request:
POST <baseUrl>/rest/testy/1/run/<testRunID>/issue/<issueID>/notes Content-type: application/json